On the characterisation of solar cells using light beam induced current
measurements
L.J Bezuidenhout, E.E van Dyk, F.J Vorster and MC du Plessis
Nelson Mandela Metropolitan University
Centre for Energy Research
Abstract
The Light Beam Induced Current (LBIC) measurement technique is used to perform
localized characterization on solar cells using a light beam as a probe. This technique
allows the determination of the local photo-response of a solar cell which enables
characterization of the spatial distribution of defects and electrical parameters. By scanning
the beam probe across a solar cell while measuring the current-voltage characteristics at
each point, a map of various cell parameters such as short-circuit current, carrier lifetime,
quantum efficiency of a solar cell and other device parameters may be extracted using this
technique.
In this study a high resolution LBIC system was designed and constructed. This paper
discusses the design of the LBIC system, the software interfacing of the data acquisition
system, local photo-response of the individual cells and LBIC maps indicating areas of
reduced efficiency or performance as a function of spatial distribution within different solar
cell technologies, including, single-crystalline (c-Si) and multicrystalline (mc-Si) Silicon. In
addition this paper also discusses the basic principle of the parameter extraction algorithm
used to extract device parameters of a solar cell.
Keywords: parameter extraction, LBIC, device parameters, photo-response, I-V
characteristics
1. Introduction
The semiconductor materials used to manufacture solar cells are not always defect free and
the defects present in the bulk and surface of these materials negatively impact the electrical
performance of the solar cells. Standard characterisation tools, such as visual inspection,
electroluminescence and infrared imaging act as complimentary techniques to characterise
the extent of these performance limiting defects. LBIC is a non-destructive technique that
focuses light onto a solar cell device thus creating a photo-generated current that can be
measured as a function of its position on the cell surface. By measuring the variation in the
photo generated current as the beam probe is scanned across the cell, the performance
limiting defects can be identified and therefore characterised.
To determine the device parameters such as the parasitic resistances, diode ideality factor
and saturated current of the photovoltaic devices a parameter extraction routine was
developed. The routine is based on the principle of minimizing the area under the I-V curve
from the experimental data collected and the model of the diode equation based on a set of
initial guesses for each parameter. The parameters extracted allow for the characterisation
of the defects present in the solar cells.
1.1. Objectives
The objective of this investigation is to design and construct an LBIC system to identify
performance degrading defects in solar cells. The primary aim is to create a device
parameter extraction routine that best approximates the parameters. By extracting these
device parameters the solar cell can be electrically characterised and thus the performance
of the device can be improved.
2.
Proposed model or Conceptual method
A solar cell consists of a semiconductor diode, which is formed by joining n-type and p-type
semiconducting materials. Semiconducting solar cells are generally represented by the onediode or two-diode equivalent models as shown in figure 1.
The I-V characteristic of a solar cell is described by the two diode equation (Thantasha, N.
2010).
-1) -
-1) -
……….1
Where I01 is the ideal saturated current, I02 is the non-ideal saturated current, n1 and n2 the
diode ideality factors, IL the illuminated current and T the temperature.
Figure 1: Equivalent cell model (Macabebe, E. 2009)
When the semiconducting diode in the solar cell is subjected to light, the incoming photons
that have enough energy will excite the electrons from the valence band to the conduction
band leaving holes in the valance band. In the region of the junction an electric field will
sweep the excess electrons to the n side of the junction, resulting in an excess of charge
and thus an open circuit voltage (Voc) can be measured. The short-circuit current (Isc) is a
function of the concentration of excited charge carriers which is related to the incident
intensity of the light.
To accurately explain the I-V characteristics of a photovoltaic module the resistance due to
defects of the cell Rsh and the series resistance Rs cannot be ignored as series resistance
reduces the voltage produced by the cell, which then reduces the performance of the solar
cell. The shunt resistance due to crystal impurities which produces shunt paths (Gxasheka,
A. 2008), giving rise to shunt currents (Ish), that lead current away current from their intended
direction and therefore decreasing the performance of the cells. For a good solar cell Rsh
must be infinitely large and therefore Ish negligible.
The solar cell device performance is described in terms of the parameters derived from the
light I-V curve shown in figure 2. The extraction routine used to obtain these device
parameters makes use of the area between the I-V curve from the measured data set and
the diode equation modelled with initial guesses for each parameter that lies within the
theoretical range.
Figure 2: Light I-V characteristics of a solar cell
The proposed model minimizes the area under the curve between the I-V curve obtained
from the data and the model. Since the raw data is piece-wise smooth, which makes
integration over such a region very difficult, an nth degree polynomial was created using the
least-square fit method that accurately fits the experimental I-V data and thus making
integration simpler. By keeping one parameter fixed at a time and using the initial guesses
for the other parameters we integrate over the area between the polynomial and the model,
where the initial guesses are updated by the values obtained from the model each time.
To minimize the area under the curve with respect to each parameter, the best fit model was
obtained by setting the derivative of the resulting integral to zero, thus,
0
, , , , ………2
To iteratively solve this equation Newton’s method was used to determine the roots of
equation 2. The method takes advantage of the ratio between the function and small
changes to the solution as I changes with respect to each parameter and is given by
equation 3.
..…….3
The method yields a good approximation for n, I0, and Rs, however, problems occur with IL
and Rsh Integrating the diode equation and taking the derivative with respect to each
parameter, IL goes to zero and Rsh goes to infinity. Infinitely large values for Rsh are expected
for the ideal case. Another method was thus required to determine these last two
parameters.
IL was approximated to be Isc, which is a good approximation since all the other parameters
at that point are negligible. For Rsh a set of values that surrounds the theoretical value was
chosen. By using the other parameters obtained from the model and plotting all the values of
the set for the diode equation, the value that gives the best fit to the polynomial from the set
was chosen.
3.
Research methodology
The LBIC system designed for this project consist of a laser source for current generation in
the cells at a point, beam expander, aperture, objective lens and x-y stage driven by stepper
motors as indicated in figure 3. The adjustable aperture in front of the objective lens allows
the user to vary the beam diameter incident on the sample. A Labview programme was
written to interface the data acquisition systems and the x-y stages. The flowchart
illustrating the sequence of the procedure within the Labview algorithm is given by figure 4.
Figure 3: Schematic of LBIC system
Figure 4: Flowchart illustrating Labview algorithm
By scanning the beam across the solar cell in a raster pattern while measuring photogenerated current as a function of spatial distribution, a structural image of the current
across the cell is mapped and regions of current reducing defects can be identified.
In addition, the system allows for forward and reverse biasing of the sample using an
alternating current voltage source (waveform generator). At predetermined bias-voltages the
photo-generated current is measured which allows for I-V characterisation of the cell and
subsequent device parameter extraction.
4.
Results
Single crystalline and multi-crystalline Silicon solar cells were used for analysis. The LBIC
measurements were done using a 633 nm wavelength laser beam with a spot size of
approximately 100 µm incident on the cell and 100 µm step size. Figure 5 shows an Isc map
of a single crystalline silicon solar cell. The scan shows clearly the contact fingers and other
current reducing features. The fingers acts as shading features and therefore no current is
generated (Thantasha, N. 2010). The scan indicates a scratch across the solar cell; this is
due to poor handling of the cell. Figure 6 indicates a higher resolution LBIC scan of the
circled area in figure 5. This current reducing defect could be due to impurities present in
the semiconductor material that could have been introduced during the manufacturing
processes.
Figure 5: LBIC map of cell area 15.0x20.0 mm2 at zero biasing voltage.
Figure 6: LBIC map of circled area at zero biasing voltage.
Figure 7 shows a LBIC map of the 10.0 mm x 10.0 mm multi-crystalline Si solar cell used in
this study. The LBIC scan was done with a 633 nm laser beam with a spot size of
approximately 150 µm spot size and 100 µm step sizes. Since relatively low resolutions
were used for the LBIC mapping, grain boundaries were not clearly defined. The regions
indicated by the arrows show areas of defects within the cell, some of the regions could be
grain boundaries or defects within the semiconductor material presented in the process of
manufacturing the cells.
Photoresponse map
Current
1.4
1.3
C u rren t (m A)
1.5
1
1.2
0.5
150
C
D
B
1.1
A
100
1
50
Y position (x0.1mm)
0 0
20
40
60
80
100
120
0.9
X position (x0.1mm)
Figure 7: LBIC map of a multi-crystalline Si cell, indicating regions where line scans
and I-V measurements were taken
By scanning the light beam across one axis and keeping the other axis constant a line scan
across the multi-crystalline Si solar cell was obtained at different biasing voltages as shown
in figure 8. The figure clearly shows the current drop due to the metallized shading of the
contact fingers of the cell. The lines present below Isc represent the scan taken at reverse
bias voltages while the lines above indicate scans taken at forward bias voltages. The extent
of the current reducing defects and their effect on the photo generated current at different
biasing voltages can clearly be seen by figure 8.
1.5
1
0.5
Current (mA)
Defect
-0,26V
-0.21V
-0.02V
Isc
0.09
0.18V
0
-0.5
-1
Fingers
Defect
-1.5
-2
-2.5
0
20
40
60
Position (x0.10 mm)
80
100
120
Figure 8: Line scans cross the multi-crystalline Si solar cells at different biasing
voltages
Figure 9 shows the I-V curves of the points indicated on the multi-crystalline solar cell in
figure 7, and will be used to extract the cell parameters at these points on the cell. The data
points from the I-V curve were used to obtain the device parameters by using the method
described. Parameters such as diode ideality factor (n), series resistance (Rs), shunt
resistance (Rsh), saturated current (Io) and the illuminated current were extracted and are
listed in table 1. From figure 9 the small differences in the I-V characteristics of the points on
the cell can be seen. Points A and D shows slightly better current yields than regions B and
C and this is due to the smaller shunt currents at these regions.
Current vs. Voltage
1.5
A
B
C
D
1
C u rre n t (m A )
0.5
0
-0.5
-1
-1.5
-2
-2.5
-3
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
Voltage (V)
Figure 9: I-V curve of the points A, B, C, and D indicated on figure 7
0.2
0.25
Table 1: Device performance parameters of a multi-crystalline Si solar cell.
Region
A
IL (mA)
1.3501
n
1.975
Rsh (Ω)
55.84
Rs (Ω)
2.371
I0 (mA)
-4
9.00x10
B
1.3675
1.820
49.53
1.661
8.96 x10
C
1.2267
1.797
45.90
3.034
8.93 x10
D
1.2221
1.985
60.69
2.863
8.98 x10
-4
-4
-4
The lower voltage region of the I-V curves are influenced by Rsh and the higher voltage
region by Rs. Table 1 shows that these values differ slightly and this could be due to
different inter-grain defects present at these regions, which reduce photo-generated
current (Gxasheka, A. 2008). The lower Rsh value is indicative of an increase of shunt paths
across the p-n junction of the cell, which leads the photo-generated current away from its
proposed direction, thus we expect the performance of regions B and C to be less than
regions A and D. The device parameters IL, n and I0 are also listed in the table, these have
fairly similar values for all the regions.
5.
Conclusions and recommendations
The defects present in the semiconductor materials, mainly due to impurities that occur
during the manufacturing process reduce the performance of the solar cells and it is
therefore important to be able to detect these defects. LBIC is a non-destructive method that
allows for the identification and characterisation of the defects present in the solar cells. The
LBIC system that is being developed is able to map the photo-generated current as a
function of position on the cell. By observing this current distribution map, defect regions in
the cells may be identified. The single and multi-crystalline Si solar cells showed regions of
current reducing defects that ultimately reduce the performance of the solar cell. In addition,
the LBIC system is able to measure the I-V characteristics at each point on the solar cell,
which allowed for the extraction of the device performance parameters at each
measurement point. The parameters obtained from the multi-crystalline Si cell were used to
describe the performance of the cell at various regions. Future work involves extracting
parameters over the entire cell and mapping these parameters as a function of position for a
better understanding of the performance of the solar cell.
References
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